Physics Applied to Radiology RADI R250 Fall 2003

1
Physics Applied to RadiologyRADI R250 -- Fall
2003

• Chapter 8

2
Alternating Current Review

• Alternating Current (AC)
• e- flow one way then they flow the opposite way
• graph (sine wave)
• f 60 Hz
• cycle 360o
• amplitude size of I or V
• t/c 1/60 s
• p/c 2
• pulse duration

AC source
AC Circuit

current
time
-
AC
3
Pulse Duration Review

• length of time for a single pulse
• formula
• TP 1/P x 1/f T pulse duration (sec)
• P pulses/cycle
• f frequency (Hz)

4
Pulse Problem

• How long is the pulse duration for a 6 pulse
  electric generator when operated at 60 Hz?
• TP ?? 6 pulses P 60 Hz f
• TP 1/P x 1/f
• 1/6 x 1/60
• 1/360 s .0028s 2.8 ms

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ELECTROMAGNETISM

• branch of physics that deals with the physical
  relationships between electricity magnetism
• magnetism electricity closely related
• both are results of the same basic interaction
  (the movement of electric charge)
• both studied by the forces involved
• electric nature electrostatic force
• magnetic nature magnetic force

6
Oersted's Work - 1820

• electric I moving e-
• when Ie flows, a B surrounds the conductor
• B in a plane to motion
• I B

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B -- produced by I
I

• Field concentric circles around the conductor
• Right thumb rule
• point right thumb in direction of conventional
  current
• curl fingers around conductor to determine
  direction of B

C
-

I into slide
I out of slide
8
B -- produced by I (cont.)

• Left thumb rule
• point left thumb in direction of e- flow
• curl fingers to determine direction of B

9
Electromagnetic Devices - Theory

• B around a straight wire concentric circles
  to the I

• In a loop of wire, B will pass through the loop ?
  B strength inside the loop

10
Devices (Figure 8-7, page 94)

• solenoid
• current carrying coil (helix or loops) of wire
• has a strong B inside the loops of the coil
• Results in B similar to bar magnet
• uses magnetic locks, starters, etc.

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Devices (cont.) (Figure 8-8, page 94)

• electromagnet
• current carrying coil with ferromagnetic material
  inside the coil loops
• ferromagnetic material é the B strength
• level of I can be used to vary the strength
• é I éB

Ié
Iê
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Review Oersted's work - 1820

• I creates a B around the conductor
• B is to the motion.
• Direct relationship I B
• B concentric circles around conductor
• direction
• Right thumb rule I -
• Left thumb rule Ie -

13
Faraday Henry (1831)

• If I creates a B,
• can B create I?
• Electromagnetic Induction
• process of creating I by moving a B relative to a
  conductor

14
Laws of Electromagnetic Induction

• 1. I will flow in a circuit if any part of the
  circuit is in a changing B
• No I in a stationary wire in a static B
• Factors involved
• Relative motion between conductor B
• Control magnitude of induced I
• Control direction of induced I

15
Relative Motion of Magnetic Field

• conductor moves B static

B moves conductor static
D strength of B conductor static
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Magnitude of Induced Current

• proportional to of B lines cut / time
• motion disturbs ("cuts") B lines
• disturbance I

17
Control magnitude of induced current by

• ?strength of B
• B I

?speed of motion ?v ?I
?direction of motion ? to B most I
?shape of conductor straight wire limited
I coil ?I (? loops ?I)
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Direction of Induced Current

• I direction -- Right hand rule
• point thumb in direction of conductors motion
• point fingers in direction of B
• palm of hand faces in direction of I flow

in above example I flows into page (e- flow
out of page)
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2nd Law of Electromagnetic Induction (Lenzs Law)

• induced I flows in direction opposing inducing
  action
• B of induced I opposes B used to induce I

N
S
à
ß

• R Hand rule I into page
• R Thumb rule B w/ clockwise direction
• maintains Conservation of Energy

20
Types of Electromagnetic Induction

• 1. Self induction
• opposition to I flow in a circuit as B builds or
  decays around that circuit
• follows from Lenz's Law (text page 115)
• process
• when I starts/stops, B around conductor D
• D B creates electromagnetic induction.
• induction creates an opposite effect on I

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Self Induction (cont.)
EMI
EMI
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Mutual Induction

• creation of a I in a 2nd conductor w/D B from 1st
  conductor
• 1) primary 1st conductor has D B
• a. AC source b. primary coil

2) secondary 2nd conductor gets an induced
I c. insulator d. secondary coil e. load
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Applications of EM Induction

• electromechanical devices
• generator
• device to convert mechanical E to electrical E
• motor
• device to convert electrical E to mechanical E
• electromagnetic device
• transformer
• device to transfer or adjust the V or I in a
  circuit

24
Generator (Text page 97) converts mechanical E
to electrical E

• 1. wire coil between B poles
• 2. operation
• -- coil is mechanically turned in B
• -- as coil moves it cuts through B
• -- current induced

N
S
S
N
25
AC Generator Operation
90º to 180º
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Motor (Text figure 8-16, pages 98)
converts electrical energy to mechanical energy

• 1. components same as generator

2. operation -- I is passed through the coil --
B of the I interacts with permanent B causing
coil to move
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Motors (types)

• synchronous
• coil rotates at same frequency as current (60 Hz)
• used in timing circuits in older machines
• induction (figure 8-17. page 98)
• stator and rotor
• uses electromagnets to create magnetic field to
  interact with current's magnetic field
• type used to rotate anode on x-ray tube

28
Transformer electromagnetic device (mutual
induction)

• 1. components
• -- 2 adjacent coils
• -- coils not physically connected to each other

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Transformer (cont.)

• 2. operation
• a) AC in primary coil produces D B
• b) Secondary coil receives a D in I V

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Transformer Turns Ratio

• ratio of the of turns in the secondary coil to
  the of turns in the primary coil

• numerical factor indicating relative change in PD
  across a transformer
• TR gt 1 éV (step up)
• TR lt 1 êV (step down)

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Transformer TR Problem

• What is the turns ratio of a transformer that
  has 74,500 primary coil loops 18,625 secondary
  coil loops?
• What does this TR indicate about the
  transformer?
• This is a step down type transformer that will
  have 25 of the voltage on the secondary compared
  to the voltage on the primary.

32
Transformer Law (change in voltage in a
transformer)

• D in V is directly proportional to the ratio of
  the of turns in the secondary to the of turns
  in the primary
• Formula

NS secondary coil turns NP primary coil
turns VS secondary voltage VP primary
voltage direct relationship
33
Transformer Voltage Problem

• A transformer has 650 turns in its primary coil
  4200 turns in the secondary coil. If an AC
  source with a 220V PD is attached to the primary
  coil, what is the PD in the secondary?

34
Transformer Current

• Current in a transformer will be inversely
  proportional to the TR of the transformer
• formula

IP primary coil current IS secondary coil
current

• I vs. V inverse relationship

35
Transformer Current Problem

• What is the output I of a transformer that has
  74,500 primary coil loops 18,625 secondary coil
  loops when the primary side is provided with 28A,
  220V power?

36
TRANSFORMER POWER

• power is same on primary secondary
• PP PS
• IPVP ISVS
• inverse relationship between I and V
• assumes ideal transformer (no loss from primary
  to 2ndary)
• Copper Resistance loss (resistance of wires in
  coil)
• Hysteresis loss (continual ?? I adds resistance)
• Eddy current loss (Lenzs law)
• Conservation of Energy

37
Transformer Power Problem

• A transformer with a TR of 2.75 uses 220 V
  draws 12 amps. What is the power on the primary
  side? What is it on secondary side?
• PP?? VP 220V IP 12A
• PP IP x VP
• 12A x 220V
• 2640 W 2600 W
• PS PP 2600 W

38
Transformer V vs. I

• Relationship between V I is inverse
• since IPVP ISVS (PPPS)

P IP VP IS VS 100 10 10 5 20 50 2 25 50 1 4 4
1 2 2
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Types of Transformers

• Based on TURNS RATIO

1. step-up turns ratio gt 1 VS gt VP IS lt IP
2. step-down turns ratio lt 1 VS lt VP IS gt IP
40
Transformer Types (cont.) Based on STRUCTURE OF
COILS
1. Place arrowheads on the sketches below to
indicate the magnetic field direction for the
current or electron flow indicated. a. Current
into the page b. electrons into the page c.
electron flow through loop

• 1. air core
• -- inside area of coil is empty
• -- inefficient induction

2. open core -- ferromagnetic material inside
coils -- ?B ?induction
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Transformer Types (cont.)

• 3. closed core
• -- ferromagnetic ends connected
• -- B induction

4. shell -- lazy square eight -- overlap of
coils on same ferromagnetic core
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Transformer Types (cont.)

• 5. autotransformer
• -- one coil acts as both primary secondary
• -- works on self-induction
• -- taps allow selection of a variable TR
• -- all other transformers have fixed TR